Theorem necom 2498

Description: Commutation of inequality. (Contributed by NM, 14-May-1999.)

Assertion

Ref	Expression
necom	|- ( A =/= B <-> B =/= A )

Proof of Theorem necom

Step	Hyp	Ref	Expression
1		eqcom 2236	. 2 |- ( A = B <-> B = A )
2	1	necon3bii 2452	1 |- ( A =/= B <-> B =/= A )

Syntax hints:   <-> wb 105   =/= wne 2414

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-5 1496  ax-gen 1498  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-ne 2415

This theorem is referenced by:  necomi  2499  necomd  2500  difprsn1  3835  difprsn2  3836  diftpsn3  3837  fndmdifcom  5786  fvpr1  5890  fvpr2  5891  fvpr1g  5892  fvtp1g  5894  fvtp2g  5895  fvtp3g  5896  fvtp2  5898  fvtp3  5899  netap  7570  2omotaplemap  7573  zltlen  9659  nn0lt2  9662  qltlen  9975  fzofzim  10531  flqeqceilz  10684  isprm2lem  12817  prm2orodd  12827  tridceq  16858